Analysis of the nonlinear vibration of a two-mass–spring system with linear and nonlinear stiffness

An analytical approach is developed for areas of nonlinear science such as the nonlinear free vibration of a conservative, two-degree-of-freedom mass–spring system having linear and nonlinear stiffnesses. The main contribution of this research is twofold. First, it introduces the transformation of two nonlinear differential equations for a two-mass system using suitable intermediate variables into a single nonlinear differential equation and, more significantly, the treatment of a nonlinear differential system by linearization coupled with Newton’s method. Secondly, the major section is the solving of the governing nonlinear differential equation where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using a first-order variational approach. The aforementioned approach proposed by J.H. He, who actually developed the method, is exactly He’s variational method. This approach is an explicit method with high validity for resolving strong nonlinear oscillation system problems. Two examples of nonlinear two-degree-of-freedom mass–spring systems are analyzed, and verified with published results and exact solutions. The method can be easily extended to other nonlinear oscillations and so could be widely applicable in engineering and science.     

Positron annihilation studies in ZnO nanoparticles

We report results on positron annihilation spectroscopic (PAS) studies using lifetime and coincidence Doppler broadening techniques in zinc oxide (ZnO) nanoparticles (4 to 40 nm) synthesized by solid state pyrolytic reaction followed by annealing in the temperature range of 200 ^°C to 800 ^°C. Positron lifetime in the nanoparticles are observed to be higher than bulk lifetime in all the cases. Theoretical calculation of lifetime indicates the presence of either Zn or (Zn, O) vacancy clusters which migrate and anneal out at high temperature. Comparison of ratio spectra from coincidence Doppler broadening measurement and calculated electron momentum distribution indicates the presence of either Zn or (Zn, O) vacancies. In addition, photoluminescence (PL) measurements have been carried out to examine the role of defects on the intensity of emission in the visible region.     

Transverse energy per charged particle and freeze-out criteria in heavy-ion collisions

In relativistic nucleus–nucleus collisions the transverse energy per charged particle, ET/Nch$E_T/N_{\mathrm{ch}}$, increases rapidly with beam energy and remains approximately constant at about 800 MeV for beam energies from SPS to RHIC. It is shown that the hadron resonance gas model describes the energy dependence, as well as the lack of centrality dependence, qualitatively. The values of ET/Nch$E_T/N_{\mathrm{ch}}$ are related to the chemical freeze-out criterium E/N≈1 GeV$E/N\approx 1\text{GeV}$ valid for primordial hadrons.     

A simple coumarin-based colorimetric and ratiometric chemosensor for acetate and a selective fluorescence turn-on probe for iodide

A novel colorimetric and ratiometric anion chemosensor bearing phenylhydrazone- coumarin moieties as recognition sites was rationally designed and synthesized. Upon addition of a series of anions to receptor R1 in 1:1 CH₃CN/H₂O, only the appearance of the solution of receptor R1 with acetate showed a color change from pale yellow to purple (bathochromic shift from 411 to 573 nm) which can be detected by the naked eye at parts per million. The probe R1 developed herein represents the rational design of a fluorescence turn-on probe for iodide, which is a notorious fluorescence quencher due to the heavy atom effect. The probe developed herein represents the fluorescence amplified probe for iodide.     

Single Amino-Acid Based Self-Assembled Biomaterials with Potent Antimicrobial Activity

The design and development of soft biomaterials based on amino acid and short-peptide have gained much attention due to their potent biomedical applications. A slight alteration in the side-chain of single amino acid in a peptide or protein sequence has a huge impact on the structure and function. Phenylalanine is one of the most studied amino acids, which contains an aromatic phenyl group connected through a flexible −CH₂− unit. In this work, we have examined whether flexibility and aromatic functionality of phenylalanine (Phe) are important in gel formation of model gelator Fmoc-Phe-OH or not. To examine this hypothesis, we synthesized Fmoc-derivatives of three analogues unnatural amino acids including cyclohexylalanine, phenylglycine, and homophenylalanine; which are slightly varied from Phe. Interestingly, all these three new analogues formed hydrogels in phosphate buffer at pH 7.0 having different gelation efficacy and kinetics. This study suggests that the presence of aromatic side-chain and flexibility are not mandatory for the gelation of this model gelator. Newly synthesized unnatural amino acid derivatives have also exhibited promising antimicrobial activity towards gram-positive bacteria by inhibiting cellular oxygen consumption. We further determined the biocompatibility of these amino acid derivatives by using a hemolysis assay on human blood cells. Overall studies described the development of single amino acid-based new injectable biomaterials with improved antimicrobial activity by the slight alteration in the side-chain of amino acid.     

A simple coordinate space approach to three-body problems — Examples: Halo nucleus and double-λ hypernucleus

We show how to treat the dynamics of an asymmetric three-body system consisting of one heavy and two identical light particles in simple coordinate space variational approach. The method is constructive and gives an efficient way of resolving a three-body system to an effective two-body system. It is illustrated by explaining the structural properties of some nuclei of current interest, namely halo nuclei and double-λ hypernuclei. The ansatz used here may be of value in a number of three particle problems of similar nature.     

Reactive chemical dynamics through conical intersections

Reaction dynamics of prototypical, D + H₂ and Cl (²P) + H₂, chemical reactions occurring through the conical intersections of the respective coupled multi-sheeted potential energy surfaces is examined here. In addition to the electronic coupling, nonadiabatic effects due to relativistic spin-orbit coupling are also considered for the latter reaction. A time-dependent wave packet propagation approach is undertaken and the quantum dynamical observables viz., energy resolved reaction probabilities, integral reaction cross-sections and thermal rate constants are reported.     

Synthesis and characterization of some binuclear metal complexes with a pentadentate azodye ligand: An experimental and theoretical study

A novel series of binuclear complexes with Mn(II), Co(II), Ni(II), Cu(II), Zn(II), and Cd(II) ions derived from a pentadentate azo dye ligand (H₃L) was synthesized and structurally investigated by various physicochemical analyses, namely, scanning electron microscopy, transmission electron microscopy, NMR, UV–visible spectroscopy, and Electron-Spin Resonance (ESR) studies. The infrared spectral data revealed characteristic bands due to ν(N=N) and ν(C=O) at 1606 and 1631 cm⁻¹ in the free ligand. However, their positions shifted and appeared at ~1564 and ~1592 cm⁻¹ on coordination, suggesting the involvement of carbonyl oxygen and azo nitrogen in complex formation. The spectral data suggested octahedral geometry for the complexes. The kinetic parameters such as order and activation energy were determined from the thermal decomposition values. X-ray powder diffraction analysis showed the orthorhombic nature of the cadmium complex. Furthermore, Density functional theory (DFT) calculations were also recorded to describe the insight bonding. The synthesized compounds were tested for in vitro antibacterial activity against K. aerogenes, S. aureus, B. acidoterrestris, E. coli, and V. cholerae strains by the cup-plate method. In addition, the interactions that occurred in the protein–ligand complexes have been predicted by docking analysis.